The present invention relates generally to design optimization methodologies, and relates in particular to design methodologies for developing designs of structures to support a mass with a minimum amount of material.
The design of minimal material (and therefore light-weight) structures is a subject of central importance in the development of a very wide range of products from fighter aircraft to wheel chairs. The design of absolute minimum weight structures requires the identification of an optimal topology of the structural members. For a limited number of loading configurations, analytic methods have been applied to identify optimal topologies. For more general loading configurations however, the optimal topology cannot be determined analytically and numerical procedures become necessary. In recent years, researchers have developed topology optimization schemes that utilize finite element analyses (FEA) to evaluate candidate topologies. Through iterative finite element analyses, these schemes have been shown to converge to known optimal topologies. Various commercially available computer software programs exist for performing FEA.
In particular, the homogenization method has been proposed for generating optimal topologies based on minimization of structural compliance for a given design volume. Homogenization methods include the classic homogenization methods, artificial material models or Solid Isotropic Material Penalization (SIMP) methods. In an alternate approach, referred to as Evolutionary Structural Optimization (ESO), inefficient material in the design domain is removed iteratively. The ESO scheme is a relatively simple algorithm that may be readily implemented in commercial finite element software. Studies have revealed however, that while the ESO method does provide reasonable results in some simple test cases, in more complicated problems it has been shown to fail to provide the optimal topology. The homogenization method is more sophisticated than the ESO but, due to the use of a unique variational principal and the addition of specialized constraint equations, it is not amenible to being incorporated in standard finite element software. Topology optimization methods incorporating features of both these methods are called hybrid methods.
In the topology optimization methods described above, the optimal topologies are generated based on design variables computed over an FEA element, which leads to numerical instabilities such as checkerboarding and mesh dependency, and node based approaches have been proposed to address this where material density distribution is defined as a nodal variable. The tedious computations involved in determination of effective Young's modulus and the need for customized finite element codes, pose significant limitations to homogenization methods. Evolutionary optimization methods, where least stressed elements were removed successively from the design domain, have gained popularity as these methods are simpler to implement and have been shown to generate good topologies utilizing standard finite element codes. Other conventional techniques include a constant weight fully stressed (CFS) method in which the total volume of material is held constant. An advantage of this method is that the density levels of elements are allowed to increase or decrease. Such methods, however, are also not immune to numerical instabilities and other limitations.
There is a need, therefore, for a more flexible, efficient and economical methodology for performing topology optimization analyses of structures.